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United States Patent |
5,226,728
|
Vander Heyden
|
July 13, 1993
|
Method and apparatus for measuring mass flow and energy content using a
differential pressure meter
Abstract
A method and apparatus for monitoring in real time the mass and energy flow
rate of a gas through a pipeline. The invention determines the ratio of
the mass flow rate of pipeline gas flowing through a pipeline compared to
the mass flow rate of sample gas tapped from the pipeline line. The
invention involves tapping sample gas from the pipeline and flowing the
sample gas to a capillary tube or a similar device for creating a pressure
differential in a small flow. The sample gas is maintained at
substantially the same temperature as the gas in the pipeline while the
sample gas is in the capillary tube. The sample gas flows through the
capillary tube continuously as controlled by a flow controller at a rate
that is independent of the pipeline gas flow rate. A differential pressure
cell measures the pressure differential of the sample gas across the
capillary tube and also measures the pressure differential of the pipeline
gas across an orifice in the pipeline. The mass flow ratio of the pipeline
gas flowing through the pipeline to the sample gas flowing through the
capillary tube is computed using the pressure differentials measured by
the differential pressure cell. The energy content of the pipeline gas is
determined by measuring the energy content of the sample gas and relating
that value to the mass flow ratio of the pipeline gas compared to the
sample gas. If the sample gas is a saturated hydrocarbon and is burned
with air at maximum flame temperature, the energy content of the pipeline
gas stream is mathematically related to the mass flow rate of the air and
the mass flow ratio of the pipeline gas compared to the sample gas.
Inventors:
|
Vander Heyden; William H. (Mequon, WI)
|
Assignee:
|
Badger Meter, Inc. (Milwaukee, WI)
|
Appl. No.:
|
787188 |
Filed:
|
November 4, 1991 |
Current U.S. Class: |
374/36; 73/196; 73/863.03; 73/863.61; 374/37 |
Intern'l Class: |
G01N 025/22; G01F 009/00; G01F 001/00 |
Field of Search: |
374/36,37
73/196,863.03,863.61
|
References Cited
U.S. Patent Documents
1924468 | Aug., 1933 | Stone | 73/196.
|
2067645 | Jan., 1937 | Pinkerton | 374/37.
|
2263335 | Nov., 1941 | Heinz | 374/37.
|
2574665 | Nov., 1951 | Schuller | 374/37.
|
3525259 | Aug., 1970 | Stough | 73/196.
|
3777562 | Dec., 1973 | Clingman | 374/37.
|
4062236 | Dec., 1977 | Clingman | 374/37.
|
4125018 | Nov., 1978 | Clingman | 374/37.
|
4125123 | Nov., 1978 | Clingman | 374/37.
|
4175433 | Nov., 1979 | Rikuta | 73/196.
|
4285245 | Aug., 1981 | Kennedy | 73/861.
|
4396299 | Aug., 1983 | Clingman et al. | 374/37.
|
4446748 | May., 1984 | Clingman et al. | 73/863.
|
4527435 | Jul., 1985 | Hall et al. | 73/863.
|
4562744 | Jan., 1986 | Hall et al. | 73/861.
|
4677841 | Jul., 1987 | Kennedy | 73/30.
|
4706492 | Nov., 1987 | Jones, Jr. et al. | 73/196.
|
5016482 | May., 1991 | Clingman et al. | 73/863.
|
Foreign Patent Documents |
0664033 | May., 1979 | SU | 73/196.
|
0652805 | May., 1951 | GB | 374/37.
|
2099589 | Dec., 1982 | GB | 374/36.
|
Primary Examiner: Cuchlinski, Jr.; William A.
Assistant Examiner: Gutierrez; Diego F. F.
Claims
I claim:
1. An apparatus for measuring a ratio of a mass flow rate of a pipeline gas
flowing through a pipeline compared to a mass flow rate of a sample gas
tapped from the pipeline, the pipeline having a first device means for
producing a pipeline gas pressure differential, the apparatus comprising:
a second device means for producing a sample gas pressure differential
while maintaining the sample gas at substantially the same temperature as
the pipeline gas;
means for routing the sample gas to the second device means;
means for measuring the pipeline gas pressure differential as the pipeline
gas flows through the first device means;
means for measuring the sample gas pressure differential as the sample gas
flows through the second device means;
a flow controlling means located downstream of the second device means for
maintaining a sample gas flow rate through the second device means
independent of the pipeline gas pressure differential; and
a control means for comparing the sample gas pressure differential with the
pipeline gas pressure differential in order to obtain the mass flow rate
ratio.
2. An apparatus as recited in claim 1 further comprising a pressure
regulator located downstream of the second device means and upstream of
the flow controlling means for reducing the pressure of the sample gas
before it flows to the flow controlling means.
3. An apparatus as recited in claim 1 wherein the control means determines
the mass flow ratio in accordance with the following function:
##EQU33##
where K is a constant, Y.sub.o is the expansion factor for the pipeline
gas, C.sub.o is the discharge coefficient for the first device means,
Y.sub.C is the sample gas expansion factor, C.sub.C is the discharge
coefficient for the second device means, .DELTA.P.sub.o is the pressure
differential of the pipeline gas across the first device means in the
pipeline and .DELTA.P.sub.c is the pressure differential of the sample gas
across the second device means.
4. An apparatus as recited in claim 3 wherein the flow controlling means
periodically varies the sample gas molar flow rate between two preselected
molar flow rates and the apparatus further comprises a sample gas flow
meter located downstream of the second device means and upstream of the
flow controlling means.
5. An apparatus as recited in claim 3 wherein the second device means is a
first tortuous path capillary tube.
6. An apparatus as recited in claim 5 wherein the flow controlling means
has a second tortuous path capillary tube.
7. An apparatus as recited in claim 3 further comprising a pressure
transducer to measure the absolute pipeline pressure P.sub.O to determine
the ratio of the expansion factor for the pipeline gas, Y.sub.o, compared
to the sample gas expansion factor, Y.sub.C.
8. An apparatus for measuring the energy flow rate of a pipeline gas
through a pipeline, the pipeline having a first device means for producing
a pipeline gas pressure differential, the apparatus comprising:
a second device means for producing a sample gas pressure differential
which maintains the sample gas at substantially the same temperature as
the pipeline gas;
means for routing the sample gas to the second device means;
means for measuring the pipeline gas pressure differential as the pipeline
gas flows through the first device means;
means for measuring the sample gas pressure differential as the sample gas
flows through the second device means;
a flow controlling means located downstream of the second device means for
maintaining a sample gas flow rate through the second device means that is
independent of the pipeline gas pressure differential;
means for determining the energy flow rate of the sample gas; and
a control means for comparing the sample gas pressure differential with the
pipeline gas pressure differential in order to obtain a mass flow rate
ratio of the pipeline gas to sample gas and for obtaining the energy flow
rate of the pipeline gas from the energy flow rate of the sample gas and
the mass flow rate ratio.
9. An apparatus as recited in claim 8 wherein the means for determining the
energy flow rate of the sample gas comprises:
a burner for burning the sample gas with air to form a flame; and
a means for maximizing the flame temperature.
10. An apparatus as recited in claim 9 further comprising an air mass flow
meter for measuring the air mass flow rate of the air burning the sample
gas.
11. An apparatus as recited in claim 10 wherein the control means
determines the energy flow rate of the pipeline gas in accordance with the
following function:
##EQU34##
where K is a constant, .DELTA.P.sub.O is the pipeline gas pressure
differential, .DELTA.P.sub.c is the sample gas pressure differential,
Y.sub.o is the expansion factor for the pipeline gas, C.sub.o is the
discharge coefficient for the first device means, Y.sub.C is the sample
gas expansion factor, C.sub.C is the discharge coefficient the second
device means, and .omega..sub.air is the air mass flow rate.
12. A method for measuring a mass flow rate ratio of a pipeline gas through
a pipeline compared to a sample gas tapped from the pipeline, the method
comprising the steps:
measuring a pipeline gas pressure differential as the pipeline gas flows
across a first device located within the pipeline for producing the
pipeline gas pressure differential;
flowing the sample gas to a second device for producing a sample gas
pressure differential;
maintaining the temperature of the sample gas in the second device at
substantially the same temperature as the pipeline gas in the pipeline;
maintaining a substantially constant sample gas mass flow rate through the
second device independent of the pipeline gas pressure differential;
measuring the sample gas pressure differential as the sample gas flows
across the second device; and
determining the mass flow rate ratio by comparing the pipeline gas pressure
differential to the sample gas pressure differential.
13. A method as recited in claim 12 wherein the second device is a
capillary tube and a control system is used to determine the mass flow
rate ratio in accordance with the following function:
##EQU35##
where K is a constant, Y.sub.o is the expansion factor for the pipeline
gas, C.sub.o is the discharge coefficient for the first device, Y.sub.C is
the sample gas expansion factor, C.sub.C is the discharge coefficient for
the second device, .DELTA.P.sub.o is the pressure differential of the
pipeline gas across the first device in the pipeline and .DELTA.P.sub.c is
the pressure differential of the sample gas across the second device.
14. A method as recited in claim 13 further comprising the step of
periodically varying the sample gas molar flow rates between two
preselected molar flow rates to determine the ratio (C.sub.o /C.sub.r).
15. A method as recited in claim 13 wherein the second device is a first
tortuous path capillary tube and further comprising the step of flowing
the sample gas to a second tortuous path capillary tube after the sample
gas flows through the first tortuous path capillary tube to estimate the
absolute pipeline pressure P.sub.o for determining the ratio Y.sub.o
/Y.sub.c.
16. A method as recited in claim 13 wherein the ratio of the expansion
factor for the pipeline gas, Y.sub.o compared to the sample gas expansion
factor, Y.sub.C, is a function of the absolute pipeline pressure P.sub.O
and further comprising the step of measuring the absolute pipeline
pressure P.sub.O.
17. A method for measuring the energy flow rate of a pipeline gas through a
pipeline, the method comprising:
measuring a pipeline gas pressure differential as the pipeline gas flows
across a first device located within the pipeline for producing the
pipeline gas pressure differential;
flowing the sample gas to a second device for producing a sample gas
pressure differential;
maintaining the temperature of the sample gas in the second device at
substantially the same temperature as the pipeline gas in the pipeline;
maintaining a sample gas mass flow rate through the second device
independent of the pipeline gas pressure differential;
measuring the sample gas pressure differential as the sample gas flows
across the second device;
measuring the energy flow rate of the sample gas;
determining a mass flow rate ratio of the pipeline gas to the sample gas by
comparing the pipeline gas pressure differential to the sample gas
pressure differential; and
determining the energy flow rate of the pipeline gas from the energy flow
rate of the sample gas and the mass flow rate ratio.
18. A method as recited in claim 17 wherein the energy flow rate of the
sample gas is measured by:
burning the sample gas with air after the sample gas flows through the
second device; and
adjusting the air flow so that the sample gas burns at maximum flame
temperature.
19. A method as recited in claim 18 further comprising the step of
measuring the air mass flow rate of air burning the sample gas.
20. A method as recited in claim 19 wherein a control system is used to
determine the energy flow rate of the pipeline gas in accordance with the
following function:
##EQU36##
where K is a constant, .DELTA.P.sub.O is the pipeline gas pressure
differential, .DELTA.P.sub.c is the sample gas pressure differential,
Y.sub.o is the expansion factor for the pipeline gas, C.sub.o is the
discharge coefficient for the first device, Y.sub.C is the sample gas
expansion factor, C.sub.C is the discharge coefficient the second device,
and .omega..sub.air is the air mass flow rate.
21. An apparatus for measuring a ratio of a mass flow rate of a pipeline
gas flowing through a pipeline compared to a mass flow rate of a sample
gas tapped from the pipeline, the pipeline having a first device means for
producing a pipeline gas pressure differential, the apparatus comprising:
a second device means for producing a sample gas pressure differential
while maintaining the sample gas at substantially the same temperature as
the pipeline gas;
a first line connected to the pipeline upstream of the first device means
for routing the sample gas to the second device means;
a differential pressure cell means for alternately measuring the pipeline
gas pressure differential as the pipeline gas flows across the first
device means and the sample gas pressure differential as the sample gas
flows through the second device means;
a flow controlling means for maintaining a sample gas flow rate through the
second device means independent of the pipeline gas pressure differential;
a second line for routing the sample gas away from the second device means
to the flow controlling means;
a pressure regulator located in the second line for reducing the sample gas
pressure before the sample gas flows to the flow controlling means;
a third line for routing the sample gas away from the flow controlling
means; and
a control means for receiving data from the differential pressure cell
means and computing the ratio of the mass flow rate of the pipeline gas
through the pipeline compared to the mass flow rate of the sample gas
through the second device means.
22. An apparatus as recited in claim 21 further comprising a pressure
transducer mounted to the pipeline and in communication with the control
means for measuring the absolute pipeline pressure to determine the ratio
of the mass flow rates.
23. An apparatus as recited in claim 22 wherein the flow controlling means
periodically varies the sample gas molar flow rate between two preselected
molar flow rates and the apparatus further comprises a sample gas flow
meter for measuring the flow through the second line.
24. An apparatus for measuring the energy flow rate of a pipeline gas
through a pipeline, the pipeline having a first device means for producing
a pipeline gas pressure differential, and the apparatus comprising:
a second device means for producing a sample gas pressure differential
while maintaining the sample gas at substantially the same temperature as
the pipeline gas;
a first line connected to the pipeline upstream of the first device means
for routing the sample gas to the second device means;
a differential pressure cell means for alternately measuring the pipeline
gas pressure differential as the pipeline gas flows across the first
device means and the sample gas pressure differential as the sample gas
flows through the second device means;
a flow controlling means for maintaining a sample gas flow rate through the
second device means independent of the pipeline gas pressure differential;
a second line for routing the sample gas away from the second device means
to the flow controlling means;
a pressure regulator located in the second line for reducing the sample gas
pressure before the sample gas flows to the flow controlling means;
a burner for burning the sample gas with an air flow to form a flame;
a third line for routing the sample gas away from the flow controlling
means to the burner;
a temperature sensor for measuring flame temperature;
an air conduit for routing the air flow to the burner;
an air valve located in the air conduit for adjusting the air flow through
the air conduit;
an air mass flow meter for measuring an air mass flow rate through the air
conduit; and
a control means for receiving data from the differential pressure cell
means, the air mass flow meter and the temperature sensor, for
communicating with the air valve to adjust the air flow so that the flame
burns at the maximum temperature, and for computing the energy flow rate
of the pipeline gas through the pipeline.
25. An apparatus as recited in claim 24 further comprising a pressure
transducer mounted on the pipeline and in communication with the control
means for measuring the absolute pipeline pressure to determine the energy
flow rate of the pipeline gas through the pipeline.
26. An apparatus as recited in claim 24 wherein the flow controlling means
periodically varies the sample gas molar flow rate between two preselected
molar flow rates and the apparatus further comprises a sample gas flow
meter for measuring the flow through the second line.
27. A volumetric flow corrector to be used with a differential pressure
flowmeter measuring a volumetric flow rate and a pressure differential of
a pipeline gas flowing through a pipeline, that monitors the energy flow
rate of the pipeline gas flowing through the pipeline, and represents the
flow of the pipeline gas in terms of an adjusted volumetric flow rate that
corresponds to a volumetric flow rate at a defined pressure and
temperature, the volumetric flow corrector comprising:
a pressure reduction device means for producing a sample gas pressure
differential which maintains the sample gas at substantially the same
temperature as the pipeline gas;
means for routing the sample gas to the pressure reduction device means;
means for measuring the sample gas pressure differential as the sample gas
flows through the pressure reduction device means;
a flow controlling means located downstream of the pressure reduction
device for maintaining a sample gas flow rate through the pressure
reduction device means that is independent of the pipeline gas pressure
differential;
a sample gas energy flow rate meter;
means for determining the energy content per unit volume of the sample gas;
and
a control means for comparing the sample gas pressure differential with the
pipeline gas pressure differential, and for calculating the adjusted
volumetric flow rate of the pipeline gas through the pipeline from the
volumetric flow rate measured by the differential pressure flowmeter from
the ratio of sample gas pressure differential compared to the ratio of the
pipeline gas pressure differential, the energy flow rate of the sample
gas, and the energy content per unit volume of the sample gas.
28. A method for monitoring the energy flow rate of a pipeline gas through
a pipeline and representing the flow of the pipeline gas in terms of an
adjusted volumetric flow rate which corresponds to a volumetric flow rate
at a defined pressure and temperature, the method comprising:
measuring a pipeline gas pressure differential and a volumetric flow rate
with a differential pressure meter;
flowing sample gas to a pressure reduction device for producing a sample
gas pressure differential;
maintaining the temperature of the sample gas in the pressure reduction
device at substantially the same temperature as the pipeline gas in the
pipeline;
maintaining a sample gas mass flow rate through the pressure reduction
device independent of the pipeline gas pressure differential;
measuring the sample gas pressure differential as the sample gas flows
across the pressure reduction device;
comparing the sample gas pressure differential to the pipeline gas pressure
differential;
measuring the energy flow rate of the sample gas;
measuring the energy content per unit volume of the sample gas; and
calculating the adjusted volumetric flow rate of the pipeline gas through
the pipeline from the volumetric flow rate of the pipeline gas measured by
the differential pressure meter, the ratio of the sample gas pressure
differential to the pipeline gas pressure differential, the energy flow
rate of the sample gas, and the energy content per unit volume of the
sample gas.
29. An apparatus for measuring a ratio of a mass flow rate of a pipeline
gas flowing through a pipeline compared to a mass flow rate of a sample
gas tapped from the pipeline, the pipeline having an orifice through which
the pipeline gas flows, the apparatus comprising:
a conduit for flowing sample gas tapped from the pipeline;
a capillary located in the conduit, the sample gas being maintained at
substantially the same temperature as the pipeline gas when the sample gas
flows through the capillary;
means for measuring a pipeline gas pressure differential as a pipeline gas
flows through the orifice;
means for measuring a sample gas pressure differential as a sample gas
flows through the capillary;
a flow controller located in the conduit downstream of the capillary to
maintain a flow rate of the sample gas flowing through the capillary
independently of the pipeline gas pressure differential; and
a control means for comparing the sample gas pressure differential with the
pipeline gas pressure differential in order to obtain the mass flow rate
ratio.
Description
BACKGROUND OF THE ART
The present invention relates to instrumentation for measuring in real time
the mass and the energy flow rate of gas through a pipe. In particular, it
relates to apparatus for measuring the ratio of the mass flow rate of
pipeline gas flowing through a pipeline compared to sample gas flowing
through the apparatus. It also relates to apparatus for measuring the
energy flow rate of gas through a pipeline.
Mass and energy flow rates of gas through pipelines are normally calculated
by flow computers from contemporaneous measurements of several gas
parameters. Generally, for measuring mass flow rate, the volumetric flow
rate of the pipeline gas is measured and gas temperature, pressure, and
composition are measured to enable the gas density and, thus, the mass
flow rate to be calculated from the volumetric flow rate. The composition
of the gas is normally measured by gas chromatography. When the operating
conditions are such that the supercompressibility of the gas in the
calculation of density cannot be ignored, supercompressibility properties
are estimated from either the virial equations of state for the gas or
from precalculated correlations such as NX-19.
Knowledge of the values of the virial coefficients of particular gas
compositions is quite limited in the art, so the calculation of gas
density from the virial equations of state is not always possible.
Furthermore, correlations such as NX-19, for natural gas, are approximate
and the accuracy of extrapolations from such correlations is questionable.
It is therefore difficult to obtain accurate real time density values for
calculating the mass flow rates of gas flowing through a pipeline with
present day equipment.
When energy flow rate, in addition to the mass flow rate, is desired, the
energy content of the gas must also be determined. The energy content of
the gas (energy per unit mass or volume) can be determined either
indirectly by measuring the composition of the gas or by direct
measurements such as the stoichiometric ratio method. Once the energy
content of the gas is determined, the energy flow rate of the gas through
the pipeline can be calculated by multiplying the energy content of the
gas (e.g. BTU/lb) by the mass flow rate of the gas (e.g. lbs./hr).
Each of the measurements discussed above (volumetric flow, temperature,
pressure, and composition) are measured separately and introduce an
opportunity for measurement error. The aggregation of these measurement
errors can substantially distort mass and energy flow calculations. To
minimize measurement errors, each piece of instrumentation must be
maintained and calibrated periodically. Moreover, additional errors can be
introduced within the flow computer from calculations or inaccurate
formulas or correlations.
In U.S. Pat. No. 4,396,299, Clingman discloses a method and apparatus for
measuring the rate of energy flow of gas through a pipeline. The Clingman
invention, which flows sample gas through a calibrated capillary tube, is
able to measure the energy flow of pipeline gas through a pipeline by
sampling a constant fraction of the pipeline gas and measuring the mass
flow of air which is burned with the sample gas at maximum flame
temperature. In the Clingman invention, the mass flow rate of the sample
gas varies in direct proportion with the mass flow rate of the gas through
the pipeline. This direct variation is the basis for at least two
shortcomings of the device disclosed in U.S. Pat. No. 4,396,299.
A first shortcoming is caused by fluctuating sample gas flow. The
fluctuations cause difficulties in burning the sample gas to measure its
energy content. In the Clingman invention, the sample gas must be burned
with air at maximum flame temperature so that the energy content of the
sample gas flow is proportional to the air mass flow. If the mass flow of
the sample gas varies over a wide range, the flame is not always stable
and temperature detection may be corrupted. If this happens, the measured
energy content of the sample gas will not be accurate.
A second shortcoming caused by the direct variation of sample gas flow to
pipeline gas flow is practical in nature. In the United States, large
natural gas pipelines are normally metered using multiple parallel
metering runs so that monitoring the flow through large diameter pipes
(i.e.>12") is avoided. In Clingman's invention, each of the multiple runs
must be treated as an individual independent energy flow rate measurement
since the Clingman invention requires that the sample gas flow rate be
proportional to the flow rate of the gas flowing through each pipe being
monitored.
SUMMARY OF THE INVENTION
The present invention is a method and apparatus for determining the ratio
of the mass flow rate of pipeline gas through a pipeline compared to the
mass flow rate of sample gas tapped from the pipeline. The invention
allows this determination to be made in real time.
Sample gas is tapped from the pipeline and flows to a capillary tube, or
similar device for producing a pressure differential. While the sample gas
is in the capillary tube, the sample gas must be maintained at
substantially the same temperature as the gas in the pipe. Sample gas
flows through the capillary tube continuously as controlled by a flow
controller at a rate independent of the pipeline flow rate.
The present invention requires two measurements for determining the mass
flow ratio: a pressure differential of the pipeline gas across an orifice
located in the pipeline, .DELTA.P.sub.o, and a pressure differential of
the sample gas across the capillary tube, .DELTA.P.sub.c.
Based on the pressure differential of the sample gas across the capillary
tube, .DELTA.P.sub.c, and the pressure differential of the pipeline gas
across an orifice or similar device producing a pressure differential in
the pipeline, .DELTA.P.sub.o, the ratio of the mass flow rate of pipeline
gas through the pipeline compared to the mass flow rate of the sample gas
can be computed in a control system (e.g. a computer).
The present invention alleviates the need to consider the effects of gas
supercompressibility, temperature, pressure, density or composition
because the sample gas pressure differential is measured while the sample
gas is at pipeline conditions.
An object of the present invention is to measure the mass flow ratio
without fluctuating the flow rate of the sample gas through the capillary
tube. The present invention accomplishes this object by maintaining a flow
through the capillary tube independent of the pipeline flow with a flow
controller.
Another object of the present invention is to accurately measure the mass
flow ratio without employing additional instrumentation to directly
monitor the absolute temperature and absolute pressure of the pipeline
gas. The present invention accomplishes this object by manipulating and
monitoring the sample gas flow so that parameters necessary to accurately
determine the mass flow ratio can be computed. For instance, the invention
contemplates using a tortuous path capillary tube (or other apparatus
which will, like the tortuous path capillary tube, have discharge
characteristics at operating Reynold's Numbers similar to the discharge
characteristics of the orifice in the pipeline) and periodically varying
the sample gas molar flow rate between two preselected rates. In this
manner, the ratio of the discharge coefficient for the orifice, C.sub.o,
compared to the capillary tube discharge coefficient, C.sub.c, can be
computed. The invention also contemplates using a second tortuous path
capillary tube downstream in the sample gas flow of the first tortuous
path capillary tube. With this configuration, the absolute pipeline
pressure, P.sub.o, and thus the ratio of the expansion factor for the
pipeline gas, Y.sub.o, compared to the sample gas expansion factor,
Y.sub.c , can be computed. Both ratios (Y.sub.o /Y.sub.c)=Y.sub.r and
(C.sub.o /C.sub.c)=C.sub.r are parameters that can then be used to
accurately determine the mass flow ratio.
The present invention also contemplates using the apparatus described above
with apparatus for measuring the energy content of the sample gas to
determine the energy flow rate of combustible gas through a pipeline.
After the sample gas exits the flow controller, it can be fed to a burner
and burned with air at the maximum flame temperature. When the flame burns
at the maximum flame temperature, the energy flow rate of the sample gas
is proportional to the mass flow rate of air burning the sample gas.
The energy content of the flow of pipeline gas through the pipeline is
determined from calculations involving the air mass flow rate, the
pipeline gas pressure differential across the orifice and the sample gas
pressure differential across the capillary tube. Each of these
measurements can be made with precision.
The present invention allows accurate real time determination of the energy
flow rate of a pipeline gas through a pipeline without the need to
compensate for the effects of gas temperature, pressure, density,
composition or supercompressibility. It also allows for the energy flow
rate to be monitored accurately without substantially interfering with the
pipeline gas flow.
Another object of the present invention is to provide measurement stability
of the flame temperature and thus assure that the flame temperature is
maximized and that the flow of air burning the sample gas is proportional
to the energy content of the sample gas for saturated hydrocarbon gases.
This object is accomplished by feeding the sample gas to the burner at a
substantially constant flow rate and thereby promoting the flame to burn
at the constant height. A thermocouple measuring the flame temperature can
therefore be located in a consistent position within the flame and measure
relative flame temperature more accurately.
Yet another object of the present invention is to measure the energy flow
rate through each of the multiple pipeline runs at a metering station with
a single meter. The present invention can accomplish this object by
systematically sampling each run sequentially in time. This mode of
operation is not possible with the Clingman invention because the Clingman
invention requires that the sample gas flow rate be proportional to the
flow rate of the gas flowing through each pipe being monitored; whereas,
the present invention has no such requirements.
The foregoing objects and advantages of the present invention will appear
from the following description. In the description, references are made to
the accompanying drawings which form a part hereof and in which a
preferred embodiment of the present invention is shown by way of
illustration. Such embodiment does not necessarily represent the full
scope of the invention, however, and reference must be made therefor to
the claims for interpreting the scope of invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic drawing showing the fundamental apparatus of the
present invention;
FIG. 2 is a schematic diagram depicting the dynamic nature of pressure
differentials in pipeline gas flow;
FIG. 3 is a sectional view of a tortuous path capillary tube;
FIG. 4 is a front view of an obstruction disc;
FIG. 5 is a plot of test data showing the capillary tube discharge
coefficient (C.sub.c) as a function of Reynold's Number (Re);
FIG. 6 is a schematic diagram showing the pipeline mounted components of
the present invention;
FIG. 7 is a schematic diagram showing apparatus for determining absolute
pipeline pressure;
FIG. 8 is a flow diagram showing an iterative process for computing the
absolute pipeline pressure; and
FIG. 9 is a schematic drawing showing additional apparatus of the present
invention for measuring the energy flow rate of the gas through the
pipeline.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to FIG. 1, the present invention has a first 12 and a second port
14 for tapping pipeline gas 16 flowing through a pipeline 18 in the
direction shown by arrow 20. The pipeline 18 typically has an internal
orifice 22 and the pressure of the pipeline gas 16 changes as it flows
across the orifice 22. Other differential pressure volumetric flow
monitoring devices that produce a pressure differential and can be
calibrated, including but not limited to venturi devices or nozzles, can
be used in place of an internal orifice 22, but an internal orifice is
preferred.
It should also be noted that pressure differentials of pipeline gas 16
across an orifice 22 or other such device is dynamic in nature, and not
necessarily constant as depicted in FIG. 2. In FIG. 2, as the flow 20 of
the pipeline line gas 16 approaches the orifice 22, the gas pressure rises
80 slightly. The flow 20 is constricted to flow through the orifice 22 and
continues to constrict after it passes through the orifice until it
reaches a low pressure point 82. As the flow 20 constricts, flow speed
increases and consequently the flow pressure drops. Flow pressure also
drops due to frictional losses. As the flow 20 widens to fill the pipeline
18 downstream of the low pressure point 82, flow speed reduces and gas
pressure recovers to a value equal to the initial flow pressure, P.sub.o,
less frictional losses. Differential pressure flow meters are most
sensitive if the pressure differential measured is the initial pipeline
pressure, P.sub.o, less the pressure at the low pressure point 82. The
physical location of the low pressure point 82, however, varies
significantly with flow velocity and it is therefore preferred to monitor
the flow pressure at an intermediate flow recovery point 84, because such
a measurement is less likely to be inaccurate due to fluctuations in flow
velocity. In the art, there are three kinds of taps for measuring pressure
differentials, each for measuring the pressure at various stages after an
orifice: flange taps, vena contracta taps, and pipe taps. It should be
emphasized, however, that the present invention can be used with any type
of differential pressure flow meter, including but not limited to an
orifice plate 22, venturi, or nozzle, and without regard to the specific
pressure difference which is monitored by the meter.
Referring to FIG. 1, the first port 12 taps sample gas 24 from the pipeline
before it flows through the orifice 22. This sample gas 24 is routed to a
capillary tube 26. Capillary tubes are made in many forms and the term
capillary tube as used herein means a device for obtaining a very small
controlled flow rate. As will be apparent to one skilled in the art, the
present invention does not require that the capillary tube 26 be a
conventional capillary tube, or a tortuous path capillary tube 26'
described below. Rather, any apparatus that allows the flow of sample gas
24 and produces a pressure differential is sufficient for the present
invention.
It is preferred, however, that the capillary tube 26 be a tortuous path
capillary tube 26' as shown in FIGS. 3 and 4. Referring to FIGS. 3 and 4,
the flow of sample gas 24 through the tortuous path capillary tube 26' is
in the direction shown by arrows 61. The sample gas 24 is not able to flow
through the tortuous path capillary tube 26' as straight-line, laminar
flow because flow obstruction discs 58 obstruct the flow 61. Sample gas 24
can flow through the tortuous path capillary tube 26' only by flowing
through flow holes 59 which extends through each obstruction disc 58. Each
flow hole 59 is eccentrically located on a disc 58 and misaligned with
adjacent flow holes 59 to create a tortuous flow path through the
capillary tube 26'. A tortuous path capillary tube 26' with this sort of
configuration has a more stable discharge coefficient, C.sub.c, in the
flow regime of interest as shown in FIG. 5. Testing has shown that it is
preferred that the obstruction discs 58 be 0.060" thick and that the flow
holes 59 have a 0.010" diameter. The obstruction discs 58 should be
spaced apart a distance at least 5 to 6 times the thickness of the discs
58.
Referring again to FIG. 1, the second port 14 taps gas from the pipeline 18
after it flows through the orifice 22.
A differential pressure cell (DP cell) 28 measures a pipeline gas 16
pressure differential across the orifice 22, .DELTA.P.sub.o, and a sample
gas 24 pressure differential across the capillary tube 26, .DELTA.P.sub.c.
The DP cell accomplishes this by (i) measuring the pressure difference
between the sample gas 24 before it flows through the capillary tube 26
and the pipeline gas 16 after it flows through the orifice 22 or (ii)
measuring the sample gas 24 after it flows through capillary tube 26.
A first solenoid valve 30 is located between the DP cell 28 and the second
port 14 of the flow splitting device. A second solenoid valve 32 is
located between the DP cell 28 and the capillary tube 26 outlet 38. A
control system 36 communicates to the first 30 and second 32 solenoid
valves to coordinate them so that the second 32 valve is closed when the
first valve 30 is open and the first valve 30 is closed when the second
valve 32 is open.
The DP cell 28 detects the pressure differential across the orifice 22 when
the first solenoid valve 30 is open and the second solenoid valve 32 is
closed. The DP cell 28 detects the pressure differential across the
capillary tube 26 when the second solenoid valve 32 is open and the first
solenoid valve 30 is closed. The DP cell 28 provides an electrical signal
34 in direct proportion to the measured pressure differential to the
control system 36.
In the preferred embodiment, the control system 36 is an electrical system
utilizing conventional switching techniques to operate the instrumentation
in accordance with the procedures of the invention. If desired, the
control system 36 may employ conventional solid state microprocessor
techniques, such as: an electronic timing device or clock, an
analog-to-digital converter, output signal amplifiers, storage memory for
a control program, an arithmetic unit for dividing, and the like.
The present invention preferably employs a single DP cell 28, but using
more than one DP cell 28 is possible. By using two DP cells 28, each DP
cell 28 can individually monitor a separate pressure drop: one to
continuously monitor the pressure drop across the orifice 22 and one to
continuously monitor the pressure drop across the capillary tube 26. A
single DP cell 28 is preferred, however, because it provides common mode
rejection.
Referring to FIG. 1, zero offset error in the DP cell 28 can be completely
eliminated by adding a line 42 with a third solenoid valve 44 for flowing
sample gas 24 around the capillary tube 26. When the third 44 solenoid
valve is opened, the pressure across the DP cell 28 is zero and the zero
offset is the residual DP cell signal 34. The zero offset is communicated
to the control system 36 where it is stored and subtracted from subsequent
DP cell signals 34 taken when the third solenoid valve 44 is closed. In
this manner, offset error is totally eliminated. The third solenoid valve
44 can be opened periodically for calibration.
A flow controller 40 for maintaining a substantially constant flow of
sample gas 24 from the capillary tube 26 is located downstream of the
capillary tube 26 and downstream from the branch 86 of the sample line
where the second solenoid valve 32 is attached. Flow controllers are known
in the art and an electronically adjustable pressure regulator followed by
a capillary tube is suitable for this application. A pressure regulator 39
can be installed in the sample gas 24 line after the point 86 and before
the flow controller 40 to reduce the pressure of the sample gas 24 at the
flow controller 40.
The sample gas 24 must be maintained at a temperature substantially equal
to the temperature of the pipeline gas 16 when it is in the capillary tube
26. If the temperature of the sample gas 24 is maintained at substantially
the same temperature as the pipeline gas 16, the need to compensate the
effects of supercompressibility can be avoided since gas density is
maintained in the sample gas 24.
Referring to FIG. 6, the preferred method of maintaining the proper sample
gas 24 temperature within the capillary tube 26 involves routing the
sample gas 24 to the capillary tube 26 through a serpentined line 25. Both
the serpentined line 25 and the capillary tube 26 are mounted in intimate
contact with the outside surface of the pipeline 18. Insulation 27 should
be placed around the serpentined line 25, the capillary tube 26 and the
pipeline 18 to facilitate temperature equalization. With this
configuration, the temperature of the sample gas 24 within the capillary
tube is maintained at substantially the same temperature as the
temperature of the gas 16 flowing through the pipeline 18.
There are other, less preferred, methods for maintaining the proper sample
gas 24 temperature within the capillary tube 26. One such method is to
insert the capillary tube 26 into the pipeline 18.
It is not necessary to maintain the sample gas 24 temperature as
substantially equal to the temperature of the gas 16 flowing through the
pipeline 18 after the sample gas 24 exits the capillary tube 26. For that
reason, the components of the invention which are not shown to be mounted
on or at the pipeline 18 in FIG. 6 are pipeline mounted, but rather wall
mounted.
An arching sample gas feed 65 along with a valve 64 and a valve 66 are used
to remove debris entering the sample line at port 12. The low velocity in
the rising section containing the valve 64 precludes particles from
reaching the arch in the arching sample gas feed 65. Instead, the
particles fall into a lower section of the pipe containing the valve 66.
Periodically, the valve 66 can be opened to blow the collected debris from
the lower section of the pipe through a blow hole 67.
A filter 35 is also installed on the arching sample gas feed 65 to remove
debris from the sample gas 24 line. If the filter 35 becomes clogged, the
invention may become ineffective so line 37 is installed around the filter
35 with an in-line solenoid valve 45. Periodically, valve 45 is opened,
and the DP cell 28 in effect measures the additional pressure drop across
the filter 35. The pressure drop across the filter 35 as measured can be
used to correct the differential pressure valves across the capillary tube
26 that are measured by the DP cell 28 during operation. If the pressure
drop across the filter 35 is too large, the filter should be replaced.
The mass flow rate of pipeline gas 16 through the orifice 22 in the
pipeline 18 can be represented by:
##EQU1##
where F.sub.o is the orifice 22 scaling constant, E.sub.v is the velocity
approach factor, Y.sub.o is the expansion factor for the pipeline gas 16,
C.sub.o is the orifice 22 discharge coefficient, .rho..sub.o is the
density of the pipeline gas 16 and .DELTA.P.sub.o is the pipeline gas 16
pressure differential.
The orifice scaling constant, F.sub.o, and the velocity approach factor,
##EQU2##
are constants that depend on orifice geometry. For example, .beta., for a
circular orifice in a circular pipe, is defined as d/D where d is the
diameter across the orifice and D is the diameter of the pipe.
The gas expansion coefficient, Y.sub.o, and the orifice discharge
coefficient, C.sub.o in Eq. (1) can, however, vary with the pipeline gas
16 pressure or flow rate. The expansion coefficient, Y.sub.o, for orifice
22 plates can be represented as:
##EQU3##
where P.sub.o is the absolute pressure of the pipeline gas 16, and k is
the isentropic exponent of the gas 16.
The orifice discharge coefficient, C.sub.o, is usually, and properly
defined as a function of Reynold's Number,
##EQU4##
where .rho. is gas density, V is flow velocity, D is the pipe diameter or
other characteristic length of the flow field, and .mu. is the dynamic
viscosity of the gas 16). The standard AGA-3 form for representing the
discharge coefficient, C.sub.o, is:
##EQU5##
where R.sub.eD is the Reynold's Number of the pipeline gas 16 flow,
C.sub.io represents the discharge coefficient at infinite R.sub.eD and
K.sub.o is a coefficient for correction at finite R.sub.eD.
In both Eqs. (2) and (3), the second terms are small compared to the first
terms. In Eq. (2), the second term
##EQU6##
is normally about 0.02 as compared to unity. In Eq. (3), the second term
##EQU7##
for most orifice installations is about 0.5% of C.sub.io or less.
The mass flow rate of the sample gas 24 through the capillary tube 26 is
represented by:
##EQU8##
where F.sub.c is the capillary tube scaling constant, Y.sub.c is the
sample gas 24 expansion factor, C.sub.c is the capillary tube discharge
coefficient, .rho..sub.c is the density of the sample gas 24 in the
capillary tube and .DELTA.P.sub.c is the sample gas 24 pressure
differential as it flows through the capillary tube 26.
The form of Eq. (4) is similar to the form of Eq. (1), except that the
approach velocity factor, E.sub.v, which appears in Eq. (1) is taken to be
unity in Eq. (4) because .beta. is very small for the capillary tube 26.
The value of the capillary tube scaling constant, F.sub.c, does not depend
on the flow rate or pressure of the sample gas 24, but rather is a
constant that depends on capillary tube 26 geometry.
The sample gas 24 expansion factor, Y.sub.c, is represented by:
##EQU9##
where P.sub.c is the absolute pressure of the sample gas 24, and k is the
isentropic exponent of the sample gas 24. The form of Eq. (5) is similar
to the form of Eq. (2), except that the 0.35.beta..sup.4 term in Eq. (2)
is taken to be zero in Eq. (5) because .beta. is very small for the
capillary tube 26.
It is preferred that the capillary tube 26 be a tortuous path capillary
tube 26' as discussed above. The capillary tube discharge coefficient,
C.sub.c, for a tortuous path capillary tube 26' is represented by:
##EQU10##
where R.sub.eC is the Reynold's Number of the sample gas 24 flow, n is the
number of obstruction discs 58 within the tortuous path capillary tube
26', C.sub.ic represents a universal tortuous path capillary tube 26'
discharge coefficient at infinite R.sub.eC, and K.sub.c is a number for
correction at finite R.sub.eC.
As with Eqs. (2) and (3), the second term in Eqs. (5) and (6) are small
compared to the first terms. The second term in Eq. (5),
##EQU11##
is about 0.02 as compared to unity and the second term in Eq. (6),
##EQU12##
is about 5% of
##EQU13##
The fact that the second terms in Eqs. (2), (3), (5) and (6) are much
smaller than the first terms in these equations relaxes the necessary
accuracy in determining the value of the second terms. For instance, a 10%
error in determining a second term that has a value of only 2% of the
first term results in an overall error of 0.2%. Testing has shown that Eq.
(6) is very accurate for tortuous path capillary tubes 26'. Testing of
tortuous path capillary tubes 26' also shows that the coefficients
C.sub.ic and K.sub.c do not change with the number of obstruction discs 58
within the tortuous path capillary tube 26'.
The ratio of the mass flow rate of the pipeline gas 16, .omega..sub.o,
compared to the mass flow rate of the sample gas 24, .omega..sub.c, is
represented by dividing Eq. (1) by Eq. (4):
##EQU14##
where S is splitting variable that is .omega..sub.o /.omega..sub.c if
computed properly.
Since the pressure conditions across the orifice 22 in the pipeline 18 and
across the capillary tube 26 are substantially equivalent and the sample
gas 24 flowing through the tube 26 is maintained at substantially the same
temperature as the pipeline gas 16, the density of the sample gas 24,
.rho..sub.c, is equal to the density of the pipeline gas 15, .rho..sub.o.
The splitting variable S can be represented by:
##EQU15##
In Eq. (8), Fo, Fc, and E.sub.v are constants that can be determined from
orifice 22 and capillary tube 24 geometry. The ratios (Y.sub.o
/Y.sub.c)=Y.sub.r, the gas expansion ratio, (C.sub.o /C.sub.c)=C.sub.r,
the discharge coefficient ratio, and
##EQU16##
the differential pressure ratio depend on flow 20 conditions and are
measured or calculated to solve Eq. (8) for the mass flow ratio.
In Clingman's U.S. Pat. Nos. 4,125,123; 4,396,299, and 5,016,482, the
differential pressure ratio
##EQU17##
in Eq. (8) is forced to unity by a flow controller. The present invention
is different because it seeks to maintain the value of .DELTA.P.sub.c
independent of the pipeline gas 16 pressure differential .DELTA. P.sub.o
and measure the differential pressure ratio
##EQU18##
Since .DELTA.P.sub.c is independent of the pipeline gas 16 pressure
differential .DELTA.P.sub.o in the present invention, difficulties related
to fluctuating sample gas 24 flows through the capillary tube 26 are
eliminated.
Referring still to Eq. (8), Clingman's U.S. Pat. No. 5,106,482 further
employs a capillary tube constructed such that the expansion ratio,
(Y.sub.o /Y.sub.c)=Y.sub.r,
is always nearly unity. The present invention does not require Y.sub.r =1.
Rather, in the preferred embodiment, the present invention computes the
ratio (Y.sub.o /Y.sub.c)=Y.sub.r by the following formula:
##EQU19##
As can be seen in FIG. 1, the absolute pressure of the gas 24 at the
capillary tube 26, P.sub.c, and the gas 16 at the orifice 22, P.sub.o, are
identical (i.e. P.sub.o =P.sub.c).
When pipeline 18 pressure is high (i.e. 400 to 1000 psia), Y.sub.r is
nearly unity because .DELTA.P.sub.c and .DELTA.P.sub.o range from 0.3 to 4
or 5 psi. At lower pipeline 18 pressure, however, Y.sub.r might not be
close to unity. Y.sub.r is, therefore, computed using Eq. (9).
.DELTA.P.sub.c and .DELTA.P.sub.o are measured by the DP cell 28 and are
needed to solve Eq. (9). The value of the isentropic coefficient, k,
ranges from 1.2 to 1.4 for natural gas under the most extreme conditions.
A value of 1.3 for k can therefore be used for solving Eq. (9) without
causing substantial inaccuracies.
The absolute pipeline pressure P.sub.o =P.sub.c must be determined to solve
Eq. (9). Since Eq. (9) is a unity ratio with small correction terms in the
numerator and denominator, it is sufficient that the absolute pipeline
pressure, P.sub.o, be determined to within 5 to 10% accuracy to maintain
the accuracy in determining Y.sub.r to within a few percent. There are
several methods for measuring the absolute pipeline pressure, P.sub.o. One
method is to use a pipeline mounted pressure transducer 88 as shown in
phantom in FIG. 1. The pressure transducer 88 need not be accurate since
the pressure value P.sub.o is used in the correction term in Eq. (9).
Pressure transducers 88 suitable for this application are well known in
the art and can be purchased from Honeywell, Precision Dynamics or other
vendors.
If a tortuous path capillary tube 26' is used, which is preferred, the
preferred method for determining the absolute pipeline pressure, P.sub.o,
and thus Y.sub.r through Eq. (9), requires a second tortuous path
capillary tube 90 in connection with the flow controller 40.
Referring to FIG. 7, a flow controller 40 has a second tortuous path
capillary tube 90 for determining the absolute pipeline pressure, P.sub.o,
and an I/P converter 92. The flow controller 40 follows a molar flow meter
94. The molar flow meter 94 of the type described by Kennedy in U.S. Pat.
No. 4,285,245 issued on Aug. 25, 1981 is appropriate for use with the flow
controller 40. The sample gas 24 flows through the molar flow meter 94,
the I/P converter 92 and the second tortuous path capillary tube 90
sequentially. In response to an electrical input signal 96 from the
control system 36 (typically ranging from 4 to 20 ma direct current), the
I/P converter 92 precisely determines the sample gas 24 pressure causing
flow in a second tortuous path capillary tube 90.
Since the sample gas 24 composition is relatively consistent for the period
of time it takes the sample gas 24 to flow through the system and the two
tortuous path capillary tubes 26' and 90 are in series, the mass flow rate
through the tortuous path capillary tube 26' mounted on the pipeline 18,
.omega..sub.c, is substantially equal to the mass flow rate through the
second tortuous path capillary tube 90, .omega..sub.s. Because the
tortuous path capillary tube discharge coefficients, C.sub.c, are
identical for the two tortuous path capillary tubes, except for
considerations of the number of obstruction discs 58 in each capillary
tube, i.e. n.sub.c and n.sub.s, the absolute pipeline pressure, P.sub.o,
can be represented by:
##EQU20##
where (Z.sub.c /Z.sub.s) is the ratio of the compressibility factor of the
sample gas 24 in the pipeline mounted tortuous path capillary tube 26'
compared to the compressibility factor of the sample gas 24 in the second
tortuous path capillary tube 90, P.sub.s is the absolute pressure of the
sample gas 24 set by the I/P converter 92, .DELTA.P.sub.s is the pressure
differential across the second tortuous path capillary tube 90 (i.e.
P.sub.s -P.sub.atm). Y.sub.s is the gas expansion coefficient for the
second tortuous path capillary tube 90, and (T.sub.c /T.sub.s) is the
ratio of the absolute sample gas 24 temperature in the pipeline mounted
tortuous path capillary tube 26', T.sub.c, compared to the absolute sample
gas 24 temperature in the second tortuous path capillary tube 90, T.sub.s.
In natural gas applications, the absolute temperature ratio (T.sub.c
/T.sub.s) is normally close to unity as determined on the absolute
temperature scale. The pressure differential across the pipeline mounted
tortuous path capillary tube 26', .DELTA.P.sub.c, is determined by the DP
cell 28. The absolute sample gas 24 pressure at the second tortuous path
capillary tube 90, P.sub.s, and the pressure differential across the
second tortuous path capillary tube 90, .DELTA.P.sub.s, are set
contemporaneously by the I/P converter 92. The number of obstruction discs
58, n.sub.c and n.sub.s, are known constants.
Both the ratio of the compressibility factors (Z.sub.c /Z.sub.s) and the
ratio of the expansion factors (Y.sub.c.sup.2 /Y.sub.s.sup.2) are a
function of the absolute pipeline pressure, P.sub.o, so an iterative
process 98 is used to solve Eq. 10 for P.sub.o. The iterative process 98
is shown in FIG. 8. P.sub.o is first approximated by setting the ratios
(Z.sub.c /Z.sub.s) and (Y.sub.c.sup.2 /Y.sub.s.sup.2) equal to unity and
computing Eq. (10). The expansion ratio (Y.sub.c.sup.2 /Y.sub.s.sup.2) is
then computed using the following equation, which is similar to Eq. (9):
##EQU21##
Note that .DELTA.P.sub.c is measured by the DP cell 28 and P.sub.s and
.DELTA.P.sub.s are set by the I/P converter 92.
The compressibility ratio (Z.sub.c /Z.sub.s) in Eq. (10) is dependent on
gas composition as well as gas pressure and temperature. Since accuracy
requirements for Eq. (11) are not stringent and because natural gas
normally contains 80% or more methane, the known virial coefficients of
methane are used to compute the compressibility ratio (Z.sub.c /Z.sub.s)
without a significant loss in accuracy.
The absolute temperature ratio (T.sub.c /T.sub.s) is very close to unity
and can be assumed to be unity for the purposes of Eq. (10).
Alternatively, the absolute temperatures, T.sub.c and T.sub.s, can be
measured by temperature detectors 72 and 73 shown in phantom in FIGS. 1
and 7.
After determining the absolute temperature ratio (T.sub.c /T.sub.s) the
expansion ratio (Y.sub.c.sup.2 /Y.sub.s.sup.2), and the compressibility
ratio (Z.sub.c /Z.sub.s), the control system 36 computes Eq. (10) for a
new P.sub.o value and compares the new P.sub.o value to the previous
P.sub.o value. If the newly computed pipeline pressure, P.sub.o, differs
from the previous P.sub.o value by more than 2%, the iterative process 98
shown in FIG. 8 is not complete and the process 98 continues by computing
a new expansion ratio (Y.sub.c.sup.2 /Y.sub.s.sup.2) and compressibility
ratio (Z.sub.c /Z.sub.s) using the newly computed P.sub.o value. Iterative
P.sub.o values are computed in this manner using the iterative process 98
until the computed P.sub.o value differs from the previously computed
P.sub.o value by less than 2%.
Once the pipeline pressure P.sub.o is determined, the expansion factor
ratio Y.sub.r =(Y.sub.o /Y.sub.c) needed to solve Eq. (8) is calculated
according to Eq. (9).
In order to solve Eq. (8) for the splitting variable S, the discharge
coefficient ratio (C.sub.o /C.sub.c)=C.sub.r must also be determined. The
orifice discharge coefficient, C.sub.o, is defined in Eq. (3) and the
capillary tube 26 discharge coefficient, C.sub.c, is defined in Eq. (6).
The capillary tube 26 discharge coefficient, C.sub.c, can be determined by
using the control system 36 to periodically vary the flow of the sample
gas stream between two preselected flows. The flow controller 40 as shown
in FIG. 7, is used to measure the molar flow ratio of the sample gas
stream 24. As discussed above, it is appropriate to use the type of molar
flow meter 94 described by Kennedy in U.S. Pat. No. 4,285,245.
Pseudo discharge coefficients, based on the molar flows, can be represented
for the two preselected flows by:
##EQU22##
where C.sub.1 * and C.sub.2 * are pseudo discharge coefficients for the
capillary tube 26 at the two preselected sample gas 24 flows .omega..sub.1
* and .omega..sub.2 *. The molar flows .omega..sub.1 * and .omega..sub.2 *
are determined in the molar flow meter 94 by measuring the time, tm.sub.1
and tm.sub.2 for the pressure in a fixed volume 95 to drop between two
predetermined pressures. Accepting that .omega..sub.1 * and .omega..sub.2
* can be represented by tm.sub.1 and tm.sub.2 and dividing Eq. (12a) by
Eq. (12b) results in:
##EQU23##
The ratio of the pseudo capillary tube discharge coefficients
##EQU24##
is assumed to be equal to the ratio of the actual capillary tube discharge
coefficients
##EQU25##
for the two preselected flows, so:
##EQU26##
where R.sub.e1 and R.sub.e2 are the Reynold's Numbers for the flow through
the capillary tube 26 at the preselected flows. If the capillary tube 26
is a tortuous path capillary tube 26', which is preferred, the K.sub.c
f(R.sub.e) term in Eq. (14) is small compared to the C.sub.i term for the
normal range of operating Reynold's Number. Moreover, the two preselected
flows can be set in a ratio such that R.sub.e2 =.eta.R.sub.e1. The
function f(R.sub.e1), is then represented by:
##EQU27##
Equation (15) allows the calculation of the function f(R.sub.e1) in real
time without knowing the viscosity, .mu., of the sample gas 24.
The ratio of the Reynold's Number of the flow through the tortuous path
capillary tube 26' compared to the flow through the orifice 22 is
represented by:
##EQU28##
where D.sub.c is the effective diameter of the tortuous path capillary
tube 26' mounted on the pipeline 18 and D.sub.D is the effective diameter
of the pipeline 18. It follows that the discharge coefficient ratio,
(C.sub.o /C.sub.c)=C.sub.r is determined by solving Eq. (17) by iteration:
##EQU29##
Equation (17) is solved by iteration because the solution to Eq. (17)
depends on the splitting variable S and S as defined in Eq. (8) depends on
C.sub.o /C.sub.o =Cr. After the discharge coefficient ratio (C.sub.o
/C.sub.c)=C.sub.r is determined by iteration, the splitting variable S is
calculated in the control system 36 pursuant to Eq. (8). The splitting
variable S represents the mass flow rate .omega..sub.c /.omega..sub.o.
Referring generally to FIG. 9, the invention described above can be used
with the invention described hereafter, which is much like the method and
apparatus described by Clingman in U.S. Pat. No. 4,125,123 issued on Nov.
14, 1978 for determining the energy content of the flow of pipeline gas
16. For saturated hydrocarbon gas, the amount of air required to
completely combust gas at maximum flame temperature, i.e. stoichiometric
combustion, is precisely proportional to the energy released during
combustion. If the gas being combusted is a saturated hydrocarbon, the
energy flow rate of the sample gas 24 is represented by:
##EQU30##
where K.sub.sto is the stoichiometric proportionality constant, and
.omega..sub.air is the air flow rate. Likewise, the energy flow rate of
the pipeline gas 16 through the pipeline 18 is represented by:
##EQU31##
In light of Eqs. (8) and (18), Eq. (19) can be rewritten as:
##EQU32##
where K.sub.b is a constant.
In accordance with Eq. (20), the apparatus shown in FIG. 9 determines the
energy flow rate of the pipeline gas 16 passing through the pipeline 18.
Referring in particular to FIG. 9, sample gas 24 flows to a burner 46 after
it leaves the flow controller 40. Air is supplied to the burner 46 by an
air hose 48 and the sample gas 24 burns above the burner 46. A
thermocouple 50 which communicates to the control system 36 monitors flame
temperature. The air flowing through the air hose 48 is monitored by an
air mass flow meter 52. Air mass flow meters are old in the art and are
accurate at ambient conditions. The air flow is adjusted by an air valve
54, which also communicates with the control system 36, until the sample
gas 24 burns at maximum flame temperature. When the flame burns at the
maximum flame temperature, the energy flow rate of the pipeline gas 16 can
be determined.
The energy flow rate of the pipeline gas 16 is calculated in the control
system 36 in accordance with Eq. (20). The ratios (C.sub.o /C.sub.c) and
(Y.sub.o /Y.sub.c) are computed by the means discussed above. The value
K.sub.b is a constant and is stored in the control system 36. The other
valves in Eq. (20), .omega..sub.air, the air mass flow rate measured by
the air flow meter 52, and .DELTA.P.sub.o and .DELTA.P.sub.c, pressure
drops measured by the DP cell 28, are communicated electronically to the
control system 36 periodically.
Since the sample gas 24 is supplied to the burner 46 at a substantially
constant mass flow rate, flame lift is minimized and the flame temperature
is measured accurately. Burning at a substantially constant mass flow rate
is the present mode of the PMI (Precision Machine Products, Inc. Dallas,
Tex.) GB-2000 series of products and has operated successfully for over 15
years.
Many modifications and variations of the preferred embodiment which are
within the spirit and scope of the invention will be apparent to those
with ordinary skill in the art.
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